Proof and the Art of Mathematics: Examples and Extensions

by Joel David Hamkins

Overview

How to write mathematical proofs, shown in fully-worked out examples.

This is a companion volume Joel Hamkins's Proof and the Art of Mathematics, providing fully worked-out solutions to all of the odd-numbered exercises as well as a few of the even-numbered exercises. In many cases, the solutions go beyond the exercise question itself to the natural extensions of the ideas, helping readers learn how to approach a mathematical investigation. As Hamkins asks, "Once you have solved a problem, why not push the ideas harder to see what further you can prove with them?" These solutions offer readers examples of how to write a mathematical proofs.
     The mathematical development of this text follows the main book, with the same chapter topics in the same order, and all theorem and exercise numbers in this text refer to the corresponding statements of the main text.

Product Details

ISBN-13:	9780262362566
Publisher:	MIT Press
Publication date:	02/23/2021
Sold by:	Penguin Random House Publisher Services
Format:	eBook
Pages:	132
File size:	3 MB

About the Author

Joel David Hamkins is Professor of Logic at Oxford University and Sir Peter Strawson Fellow in Philosophy at University College, Oxford. He has published widely in refereed research journals in mathematical logic and set theory and is the creator of the popular blog Mathematics and Philosophy of the Infinite. He is a prominent contributor to MathOverflow, where he has posted more than 1,000 mathematical arguments.

Table of Contents

Preface vii

About the Author viii

1 A Classical Beginning 1

2 Multiple Proofs 9

3 Number Theory 15

4 Mathematical Induction 21

5 Discrete Mathematics 31

6 Proofs without Words 41

7 Theory of Games 49

8 Pick's Theorem 57

9 Lattice-Point Polygons 63

10 Polygonal Dissection Congruence Theorem 75

11 Functions and Relations 83

12 Graph Theory 93

13 Infinity 103

14 Order Theory 111

15 Real Analysis 117